for appropriate \(\widetilde{\Omega }\subseteq \Omega \) . Since by (REF ), \(\mathcal {D}_{\hat{\nu }_0 \underline{\hat{\nu }}}\sim \mathcal {D}_{\hat{\mu }_0 \underline{\hat{\mu }}}\) , and
\((\hat{\mu }_0) ^\ast \notin \lbrace \hat{\mu }_1,\ldots ,\hat{\mu }_n \rbrace \) 
by hypothesis, one can use Theorem A.31 [1]} to
conclude that \(\mathcal {D}_{\underline{\hat{\nu }}}\in \textrm {Sym}^n(\mathcal {K}_n)\)  is nonspecial. This
argument is of course symmetric with respect to
\(\underline{\hat{\mu }}\)  and \(\underline{\hat{\nu }}\) . Thus, \(\mathcal {D}_{\underline{\hat{\mu }}}\)  is nonspecial if and only
if \(\mathcal {D}_{\underline{\hat{\nu }}}\)  is.
